The green network design problem

(1)

7

Green Network Design Problems

Okan Dukkanci

1

, Tolga Bektas¸

2

, Bahar Y. Kara

1 1

Department of Industrial Engineering, Bilkent University, Ankara, Turkey;

2

Centre for Operational Research, Management Science and Information Systems (CORMSIS), Southampton Business School, University of

Southampton, Southampton, United Kingdom

O U T L I N E

1. Introduction 170

2. Previous Survey Papers 173

3. Green Network Design Problems 175

3.1 Operational Decision Making 175

3.1.1 The Energy Minimizing Vehicle Routing Problem 176

3.1.2 The Pollution-Routing Problem 180

3.1.3 Other Routing Problems 185

3.2 Tactical Decision Making 187

3.2.1 Location-Routing Problems 187

3.2.2 Allocation Problems 190

3.3 Strategic Decision Making 193

3.4 Other Studies 198

4. Conclusions and Thoughts on Further Research 198

(2)

1. INTRODUCTION

Supply chain management entails designing, planning, and coordi-nation activities for movement of products or delivery of services from the supplier to the customer. However, it is known that some of these activities are harmful to the environment. Taking the right steps for the design activities is critical in order that the environmental performance of a supply chains be improved, and these decisions often manifest them-selves in the form of network design problems.

Sustainability for systems is a term which is often used in lieu of “improved environmental performance” or to denote the ways in which “reduction of externalities” of the particular system can be achieved, and not necessarily in its literal meaning which has been characterized as the ability of the system to exist permanently provided that the environment around the system allows it do to so (Jaehn, 2016). In this chapter, we do not delve into such discussions and refer the reader to a fuller discussion on the issue byJaehn (2016), and take “sustainable” systems on face value as it appears in various references. What we will attempt to do, however, is to differentiate the terms “sustainable” and “green,” with emphasis being on the latter, through classification of the extant literature. We start by offering a proposed classification for sustainable logistics design problems as shown inFig. 7.1.

FIGURE 7.1 Classification for the design of the sustainable logistics networks.

7. GREEN NETWORK DESIGN PROBLEMS

170

(3)

Sustainable logistics network design can be separated into two cate-gories, namely those focusing on reducing the type or amount of logistics activities with negative environmental impacts and reducing the negative environmental impact directly (Fig. 7.1). The first category makes use of concepts such as city logistics, reverse logistics, and alternate fuel vehicles (AFVs), which aim to reduce logistics activities that have an environ-mental impact. In particular, city logistics reduces the environenviron-mental impacts of urban freight transportation within city boundaries with due consideration to economical and social impacts. The environmental effects within a city can be reduced by minimizing the number of freight vehicles traveling within the city and by optimizing the usage of these vehicles. City logistics uses two fundamental concepts to achieve this: the consolidation of loads in warehouses and the coordination of freight transportation activities (Crainic et al., 2009). Reverse logistics comprises the reuse, recycling, and disposal of waste products and packaging by arranging transportation activities (McKinnon et al., 2015). Reverse logistics allows companies to reduce emissions by transporting recycled products instead of producing or supplying them. In some studies, both forward and reverse logistics are considered simultaneously, giving rise to what is now known as a closed loop supply chain. Finally, AFVs are vehicles that run on alternative, environmentally friendly sources of fuel such as biodiesel, electricity, hydrogen, methanol, ethanol, and propane, rather than petroleum-based fuels (Davis et al., 2014). AFVs produce lower emissions compared to fuel-based vehicles.

The second main category shown inFig. 7.1, which we refer to as green network design, is a class of planning problems with the aim of reducing the environmental impacts of logistics activities. One of the prominent environmental impacts of logistics operations is the emission of green-house gases (GHGs), due to their detrimental effects on both human health and the environment. GHGs are described as gases that “emit and absorb radiation at specific wave-lengths within the spectrum of thermal infrared radiation emitted by the earth’s surface, the atmosphere itself and by clouds” as defined in the Glossary of IPCC’s 2007 Synthesis Report

(Bernstein et al., 2008). The primary GHGs include carbon dioxide (CO2)

that has been liked to global warming, nitrous oxide (N2O), methane

(CH4), water vapor (H2O), and ozone (O3). Burning fossil fuels such as oil,

natural gas, and coal emits GHGs and CO2(Bernstein et al., 2008).

Estimating or quantifying emissions of transportation activities is not straightforward. For instance, minimizing the travel distance of a vehicle does not necessarily result in minimizing fuel consumption as the latter depends on other factors, such as speed and load (Demir et al., 2014a). Such environmental factors would therefore have to be explicitly included in the estimation of emissions. Environmental impacts such as emissions have been calculated using different types of principles and models in

(4)

the literature. These models include the life cycle assessment (LCA) method, factor models, and macroscopic and microscopic fuel consump-tion models (Demir et al., 2014a).

LCA is a method used to evaluate the environmental impacts of a product from its raw material form until recycling. Although LCA does not directly model the emissions or the fuel requirements, it proposes a simple and systematic method of calculating the environmental impact of a process such as production, transportation, or disposal. This method-ology consists of four stages; goal definition and scoping, inventory analysis, impact assessment, and interpretation. The goal definition and scoping stage entails the definition of the product, process, and activities and the identification of boundaries and environmental impacts. In the second stage, resource usage and environmental releases are character-ized. The resource usage and environmental releases that are quantified are assessed during the impact assessment stage. The Eco-indicator 99, a damage-oriented method for life cycle impact assessment, is often used during this stage (Goedkoop and Spriensma, 2000). The final stage evaluates the results obtained during the second and third stages

(SAIC and Curran, 2006).

In contrast to the LCA method, the other models focus solely on transportation-related activities. In factor models, the data for travel distance or fuel consumption are collected and multiplied by certain coefficients (e.g., the emission factor), mainly used to estimate the CO2

emissions.EPA (2016)proposes several such factor models. On the other hand, macroscopic and microscopic models consider other factors that influence fuel consumption and CO2emissions, such as vehicle weight,

vehicle speed, payload, etc., in order to provide more accurate estimation of fuel consumption, and in turn CO2 emissions which are directly

proportional (Demir et al., 2014a). Macroscopic models estimate fuel consumption and CO2 emission using average aggregate network

parameters, whereas microscopic models include detailed parameters using instantaneous (e.g., second by second) measurements.

Network design problems have been studied with an explicit goal of reducing emissions in the transportation sector using these models, an aspect to which we will refer to as green. In this chapter, we present some of these problems by providing definitions, mathematical models, and practical applications. As our focus is on green network design problems, we do not provide a detailed coverage of others that have looked at sus-tainable network design problems such as AFVs, city logistics, and reverse logistics and closed loop supply chains. However, we do include papers in our survey that relate to both green network design and reverse logistics. For comprehensive surveys on reverse logistics and closed loop supply chains, we refer the reader toFleischmann et al. (1997), Srivastava (2008),

Dekker et al. (2013), and Govindan et al. (2015). In addition to these,

172

(5)

one may refer toPelletier et al. (2016)and Crainic et al. (2009)for more details on AFVs and city logistics, respectively.

The rest of the chapter is presented as follows. Section 2 presents previous survey papers on green network design.Section 3provides an extensive literature review on green network design problems and describes applications where relevant. The last section points out some future research directions.

2. PREVIOUS SURVEY PAPERS

The sudden rise of the popularity of sustainable and green supply chain design problems has led to several review articles being published in the literature (Table 7.1). One of the earlier such review papers on green supply chain management is by Srivastava (2007), who classifies the literature as those discussing the importance of the green supply chain management, those on green design, and those on green operations. The survey covers the papers until 2006, a period of time during which the relevant research focused more on reverse logistics. Sbihi and Eglese

(2010)introduce green logistics as a concept and combine it with some

combinatorial optimization problems, in particular reverse logistics, waste management, and vehicle routing and scheduling problems.

Dekker et al. (2012) present a comprehensive review on green logistics

problems within operations research, classified into those relevant to transportation, product (inventory), and facility location. Hassini et al.

(2012)present a literature review on sustainable supply chain

manage-ment and performance measures, with a particular focus on the latter.Lin

et al. (2014)present a survey on green vehicle routing problems (VRPs) by

first classifying the classical VRP, then by categorizing green VRPs, pollution-routing problems (PRPs) and those arising in reverse logistics. The authors describe green VRPs as problems that minimize energy consumption and PRPs as those that minimize GHG (particularly CO2)

emissions. The review byDemir et al. (2014a)is exclusively on green road freight transportation, where the authors identify and explain the factors that affect fuel consumption, and review the relevant fuel consumption models. They specifically focus on routing problems but also mention papers related to location problems.Brandenburg et al. (2014)provide a literature review on sustainable supply chain management, which also covers studies that deal with network design. However, they do not consider routing problems with environmental concerns. The review paper byEskandarpour et al. (2015)is one on sustainable supply chain network design, with a particular focus on optimization problems arising within this area. The authors review various studies relating to the

(6)

TABLE 7.1 Features of Existing Survey Papers

Sustainability Tool Decision

Reference CL RL AFVs GND Location Routing

Number of Common References

Srivastava (2007) ✕ C ✕ ✕ 1

Sbihi and Eglese (2010) ✕ C ✕ ✕ 0

Dekker et al. (2012) ✕ ✕ 13

Hassini et al. (2012) ✕ ✕ ✕ 3

Lin et al. (2014) ✕ C ✕ C 12

Demir et al. (2014a) ✕ ✕ ✕ C C 30

Brandenburg et al. (2014) ✕ ✕ ✕ 3

Eskandarpour et al. (2015)

✕ ✕ C C ✕ 19

Our study ✕ ✕ C C C

CL, city logistics; GND, green network design; RL, reverse logistics. ✕, not covered, , partially covered, C, fully covered.

174

II. AN APPROXIM A TION T O SUST AINABLE TRANSPO R T A TION

(7)

economical, environmental, or social impacts. The authors do not consider the papers that include any routing decisions.

AsTable 7.1shows, there does not seem to be a review that fully covers

the green network design literature where both location and routing de-cisions are included, which is the aim of this chapter. Here, we review 107 articles in detail. The last column of Table 7.1 reports the number of common references cited in the reviews above and in this review.Demir

et al. (2014a)andEskandarpour et al. (2015)are the two reviews that have

the highest number of shared references with our study, 30 and 19, respectively. However, Demir et al. (2014a) mainly focus on routing problems, whereasEskandarpour et al. (2015)only review problems that include location decisions.

3. GREEN NETWORK DESIGN PROBLEMS

The ensuing review is based on a categorization of the relevant studies based on the three classical levels of decision-making, namely opera-tional, tactical, and strategic, as depicted in Fig. 7.2, along with the number of references in each category. Operational decisions are mainly those related to routing. Tactical decisions consist of location-routing and allocation problems. Strategic decisions include studies that look at location-allocation problems. We present the relevant studies in the three main sections below.

3.1 Operational Decision Making

Most papers in this category consider routing decisions. The energy minimizing vehicle routing problem (EMVRP) byKara et al. (2007) and the pollution-routing problem (PRP) byBektas¸ and Laporte (2011)are the

(8)

two pioneering works that consider the minimization of fuel consumption in vehicle routing problems. In the following sections, we describe these two problems with the proposed mathematical formulations and those studies that extend these two problems.

3.1.1 The Energy Minimizing Vehicle Routing Problem

Kara et al. (2007)introduce the EMVRP as an extension of the classical

VRP, where the objective is to minimize a distance-weighted load function in order to minimize the total energy consumption. The EMVRP is defined on a network G ¼ (N, A) where N ¼ {0, 1, 2, ., n} is the set of nodes and node 0 is the depot. The customer set is denoted by N0¼ {1, 2,

., n} and A ¼ {(i, j): i, j ˛ N, i s j} denotes the set of arcs. The distance on arc (i, j)˛ A is denoted by dij. A fleet of m vehicles, each with a carrying

capacity Q and a tare weight Q0is available to serve customers, each of

which has a non-negative weight (demand) qi, i˛ N. The problem is to

find a set of routes for the vehicles that all start from and end at the depot, such that the total energy as modeled by the distance-weighted load function is minimized. The integer programming formulation proposed

by Kara et al. (2007) to solve the EMVRP uses a binary variable xijthat

equals 1 if a vehicle travels on arc (i, j)˛ A, and 0 otherwise. A continuous non-negative variable yij represents the total weight of the vehicle

(including tare weight) on arc (i, j) ˛ A. The proposed mathematical model is as follows: MinimizeX i˛N X j˛N fig dijyij (7.1) subject to X i˛N0 x0i¼ m (7.2) X i˛N0 xi0¼ m (7.3) X i˛N xij ¼ 1 c j˛N0 (7.4) X j˛N xij¼ 1 ci˛N0 (7.5) X j˛N yij X j˛N yji¼ qi ci˛N0 (7.6) y0i¼ Q0x0i ci˛N0 (7.7) yij Q þ Q0 qj xij cði; jÞ˛A (7.8)

176

(9)

yij ðQ0þ qiÞxij cði; jÞ˛A (7.9)

xij˛f0; 1g cði; jÞ˛A. (7.10)

The objective function(7.1)minimizes a cost function that depends on the total weight of the vehicle and the total distance traversed. Constraints

(7.2)and(7.3)set the number of vehicles to m. Constraints(7.4)and(7.5)

ensure that a vehicle arrives and leaves each node. Constraint(7.6)is the flow conservation between nodes. Constraint(7.7)ensures that the weight of the vehicle while leaving the depot equals the tare weight. Constraint

(7.8)sets an upper bound on the flows and serves as the vehicle capacity

constraints. Similarly, constraint (7.9)sets a lower bound on the weight variable.

Different versions of the EMVRP have been studied in the literature, as shown inTable 7.2, the first column of which shows the reference and the following four columns indicate the general features of the problem studied, namely the network type (single or multiechelon), the number of objectives (single or multiple), solution methods (exact “E” or heuristic “H”) and whether an application is presented or not. The next four col-umns represent the specifications of the proposed models, namely time window (TW), time-dependency (TD), simultaneous pickup and delivery (P&D), and uncertainty (U), respectively. The last four columns are rele-vant to fuel consumption, the first of which shows the type of emission model (factor, macroscopic, or microscopic) used. The remaining three columns shows whether distance (Dis), load (Loa), and Speed (Spe) are considered as a parameter “P” or decision “D” within the respective models.

Some of the problems shown in Table 7.2 are very similar to the EMVRP. For example,Xiao et al. (2012) consider minimizing fuel con-sumption in the capacitated vehicle routing problem where the fuel consumption rate is load-dependent, but the way in which it is calculated is more complex. Similarly, Fukasawa et al. (2015)model the cost over each arc as the product of the arc length and the weight of the vehicle including payload and curb weight. The authors presented two new mixed-integer programming formulations, namely an arc-load formula-tion and a set partiformula-tioning formulaformula-tion, where the latter is solved by a branch-cut-and-price algorithm.

Incorporating backhauling or simultaneous pick-up and delivery op-tions in vehicle routing may provide further reducop-tions in the environ-mental impacts of vehicle routing, given the flexibility afforded by such options in eliminating some of the transportation activities that cause CO2

emissions. One such study is byZachariadis et al. (2015), who studied a load-dependent vehicle routing problem similar to the EMVRP but extended to take into account simultaneous pick-up and delivery. This is

(10)

TABLE 7.2 Studies Related to the EMVRP

General Model Specifications Fuel Consumption

References Net. Obj. Sol. A. Case TW TD P&D U Emission Dis Loa Spe

Kara et al. (2007) Single Single E Factor P D e

Xiao et al. (2012) Single Single E& H Factor P D e

Fukasawa et al. (2015) Single Single E Factor P D e

Zachariadis et al. (2015) Single Single H U Factor P D e

Pradenas et al. (2013) Single Single H U U Micro P D P

Tajik et al. (2014) Single Single E U U U Micro P D P

Kwon et al. (2013) Single Single H Factor P D e

Kopfer et al. (2014) Single Single E Factor P D e

Xiao and Konak (2016a) Single Single E& H U U Micro&

Macro

P, D D e

Xiao and Konak (2016b) Single Single H U Macro P, D D e

Androutsopoulos and Zografos (2017)

Single Multi H U U Micro P D P

Huang et al. (2017) Single Single E& H U U Micro P D P

Suzuki (2011) Single Single E U Factor P P P

Cinar et al. (2014) Single Single E& H Factor P D e

Ubeda et al. (2011) Single Single H U U Factor P P e

Treitl et al. (2014) Single Single H U Micro P D P

Li et al. (2016) Multi Single H U U Factor P D P

Suzuki (2016) Single Multi H Factor P D e

178

(11)

modeled by assuming, for each customer i˛ N, a delivery request diand

pick-up request pi. Two non-negative continuous variables Dijand Pijare

defined to represent the delivery and pickup load carried on arc (i, j)˛ A. The model of this problem follows that of the EMVRP, where constraints

(7.6)e(7.9)are replaced by the following:

X j˛N Pij X j˛N Pji¼ pi ci˛N0 (7.11) X j˛N Dij X j˛N Dji¼ di ci˛N0 (7.12) djxij Dij ðQ diÞxij cði; jÞ˛A (7.13) pixij Pij Q pj xij cði; jÞ˛A (7.14) Dijþ Pij Q max0; pj dj; pi di xij cði; jÞ˛A (7.15)

Constraints(7.11)and(7.12)model flow conservation for both pick-up and delivery. Constraints(7.13)e(7.15)provide stronger lower and upper bounds on the flow variables to satisfy vehicle capacity constraints.

Zachariadis et al. (2015)describe local search algorithms and a

branch-and-cut method for the problem. Other relevant studies are by

Pradenas et al. (2013)and Tajik et al. (2014), who consider a VRP with

backhauling or simultaneous pick-up and delivery options.

The references mentioned above all assume the use of a homogeneous fleet of vehicles, i.e., all vehicles are identical. In contrast, one can assume a heterogeneous set of vehicles with varying characteristics.Kwon et al.

(2013), for example, is one such study that looks at the use of a carbon

trading mechanism within the problem. Kopfer et al. (2014) studied a similar problem, namely the emission minimization vehicle routing problem with vehicle categories, but without the use of a carbon trading mechanism.

The studies mentioned above also assume that vehicles travel at con-stant speed whilst traversing an arc, which may not be a realistic assumption, given that traffic conditions such as congestion are known to affect vehicle speed. One way to tackle this would be to assume that vehicle speeds vary with time, giving rise to routing problems where travel times are time-dependent. One such study is byXiao and Konak

(2016a), who extend the green vehicle routing and scheduling problem

(GVRSP) proposed byXiao and Konak (2015)with the inclusion of time-dependent travel times, time window constraints, the effect of weight on fuel consumption, and a heterogeneous fleet of vehicles. They also allow vehicles to stop on arcs at any time, which breaks away from similar studies that consider time-varying congestion. To solve the problem, the authors propose a hybrid algorithm that uses partial-mixed integer

(12)

programming and iterated neighborhood search. The same authors study a heterogeneous fleet GVRSP with a tardiness objective for which they propose a hybrid algorithm that combines a genetic algorithm and the exact dynamic programming solution technique (Xiao and Konak, 2016b). The other two studies that consider time-dependent travel times are

Androutsopoulos and Zografos (2017) and Huang et al. (2017). Some

variants of the EMVRP incorporate additional time-related constraints such as time windows (Suzuki, 2011) or a limit on tour length (Cinar et al., 2015).

One applications of the EMVRP can be found in the paper byUbeda

et al. (2011), who present a case study for Eroski, a food distribution

company, operating in the Navarre region of northern Spain. The distri-bution network consists of one depot, 15 customers, and 25 suppliers. Backhauling is used to fill stocks from the suppliers after serving the customers. The authors describe a nearest-neighbor insertion algorithm to solve the case study. The results indicate a saving of 14.9% in CO2

emis-sions for a week of distribution activities.Treitl et al. (2014)describe one application of the inventory routing problem for a petrochemical com-pany operating in south-eastern Europe. The comcom-pany operates on a network that consists of one depot, and seven regions including 45 filling stations (customers) in 27 cities. A mathematical formulation for the problem is described, which, when solved with a single objective function that only minimizes economical impacts, a 15.97% saving is achieved over a year. When environmental impacts are included in the objective func-tion, an additional saving of 1.35% is achieved.Li et al. (2016)propose a two-echelon time-constrained vehicle routing problem. The authors developed a two-stage heuristic algorithm and present a real-life appli-cation for two trucking companies operated in Shandong province of China, one with 23 city distribution centers serving 1008 customers, and the other with 10 city distribution centers serving 818 customers. The paper bySuzuki (2016)does not present a real-life problem, but considers users’ viewpoints while calculating fuel consumption for a routing problem called a practical PRP.

3.1.2 The Pollution-Routing Problem

The second main study that considers environmental impacts in the VRP is the PRP proposed by Bektas¸ and Laporte (2011), where the objective function minimizes the total cost including the driver cost and the fuel consumption and CO2emissions cost. The fuel consumption is

estimated using CMEM as the emission model, in which all parameters on a given segment of road (e.g., arc) are assumed to be constant except for load and speed, which are considered as decision variables in order to calculate emissions more accurately. One of the assumptions in this work is that vehicles travel with a speed of at least 40 km/h that is typically

180

(13)

applicable to intercity routes, i.e., urban areas and congestion speeds are not considered.

The PRP is defined on the same graph G ¼ (N, A) as the EMVRP, where, additionally, there are time windows [ai, bi] for each customer i˛N0, with

the service time at this customer denoted by ti. Also,aijis an arc specific

constant andb is a vehicle specific constant. Bektas¸ and Laporte (2011)

describe an integer linear programming formulation for the PRP, where the main routing variable xijis the same as the one defined for the EMVRP.

In addition, the continuous non-negative variables fijand vijrepresent the

total weight of the vehicle (excluding tare weight) and speed of the vehicle on arc (i, j)˛ A, respectively. The start time of service at node j ˛ N0is

denoted by yj. The total time spent on a route in which node j˛ N0is the

last visited node is denoted by sj. As the speed variables vijresult in a

nonlinear term in the objective function and the constraints,Bektas¸ and

Laporte (2011)discretize the speed into a set of levels R ¼ {0, 1, 2,., r}

and vrrepresents the average vehicle speed for a speed level r˛ R. A new binary variable zrij is defined which equals 1 if a vehicle travels with a

speed level r˛ R on arc (i, j) ˛ A, and 0 otherwise. The corresponding mathematical formulation is as follows:

Minimize X ði; jÞ˛A ðcfþ eÞaijdijwxij (7.16) þ X ði; jÞ˛A ðcf þ eÞaijfijdij (7.17) þ X ði; jÞ˛A ðcf þ eÞdijb X r˛R ðvr_Þ2_zr ij ! (7.18) þX j˛N0 psj (7.19) subject to(7.2),(7.4), (7.5), and(7.10) X j˛N fji X j˛N fij¼ qi ci˛N0 (7.20) qjxij fij ðQ qiÞxij cði; jÞ˛A (7.21) yi yjþ tiþ X r˛R ðdij=vrÞ . zr_ij Mijð1 xijÞ ci˛N; j˛N0; isj (7.22) ai yi bi ci˛N0 (7.23) yjþ tj sjþ X r˛R dj0 vr.zr_j0 L1 xj0 cj˛N0 (7.24)

(14)

X

r˛R

zrij¼ xij cði; jÞ˛A (7.25)

fij 0 cði; jÞ˛A (7.26)

zr_ij˛f0; 1g cði; jÞ˛A; r˛R (7.27) The objective function consists of two components, the first of which is the cost of fuel consumption and CO2emission represented by(7.15), and

the second is the cost of drivers shown by(7.19). Constraint(7.20)ensures flow conservation between nodes. Constraint (7.21) imposes lower and upper bounds on the flow variables and serves as a vehicle capacity constraint. Constraint(7.22)computes the service start time for each node. The time window restrictions for each customer are modeled through constraint (7.23). The total time spent on each route is calculated by constraint(7.24). Finally, constraint (7.25)ensures that only one level of speed is chosen on each arc of the graph that is traversed by a vehicle.

We now present a review of studies that are in the spirit of the PRP. These studies are summarized in Table 7.3. Initially, we focus on the studies that focus on the original version of the PRP.Demir et al. (2012)

study the PRP where the vehicles were allowed to travel slower than 40 km/h. They develop a heuristic algorithm in which the VRP with time windows is solved by an adaptive large neighborhood search, following which a speed optimization algorithm finds the optimal speed for each arc of route identified for each vehicle. Demir et al. (2014b) study the biobjective variant of the PRP, where the two (conflicting) objectives are to minimize fuel and minimize fuel consumption. Pareto solutions are identified by using the heuristic as a search engine, in conjunction with four a posteriori methods, namely a weighting method, a weighting method with normalization, the ε-constraint method, and a new hybrid method that combines the adaptive weighting and theε-constraint method. The results indicated that the hybrid one outperforms the others. One other metaheuristic for the PRP is described byKramer et al. (2015), which combines iterated local search with speed optimization procedures and integer programming optimization over a set partitioning formulation.

As for the exact methods on the PRP, Fukasawa et al. (2016) use disjunctive convex programming to develop two mixed-integer convex optimization models where the speed is kept as a continuous variable. They also develop a set of valid inequalities.Dabia et al. (2017)describe a branch-and-price algorithm to solve a variant of the PRP where the speed along all arcs of a given route is assumed to be constant. In the algorithm, the master problem is of a set-partitioning type, and where the pricing is performed through solving a speed and start-time elementary shortest path problem with resource constraints using a tailored labeling algorithm.

182

(15)

General Model Specifications Fuel Consumption References Net. Obj. Sol. A. Case TW TD P&D Unc Emis. M. Dis Loa Spe

Bektas¸ and Laporte (2011)

Single Single E U Micro P D D

Demir et al. (2012) Single Single E& H U Micro P D D

Demir et al. (2014b) Single Multi H U Micro P D D

Kramer et al. (2015) Single Single H U Micro P D D

Fukasawa et al. (2016) Single Single E U Micro P D D

Dabia et al. (2017) Single Single E U Micro P D D

Franceschetti et al. (2013)

Single Single E U U Micro P D D

Ehmke et al. (2016b) Single Single H U U Micro P D P

Franceschetti et al. (2017)

Single Single H U U Micro P D D

Koc¸ et al. (2014) Single Single H U Micro P D D

Saka et al. (2017) Single Single H U Micro P D D

Kumar et al. (2016) Single Multi H U Micro P D D

Eshtehadi et al. (2017) Single Single E U U Micro P D D

Majidi et al. (2017) Single Single H U U Micro P D D

Soysal et al. (2015a) Single Single E U U Micro P D P

Soysal et al. (2015b) Multi Single E U U Micro P D P

3. GREEN NETWORK DESIGN PR OBLEMS

183

(16)

Fuel consumption is known to be affected by congestion, particularly with the low speeds that vehicles travel at under heavy traffic conditions.

Franceschetti et al. (2013)incorporate such considerations within the PRP,

in particular time-dependent travel times, where it is assumed that there is an initial period of congestion followed by free-flow traffic conditions, and look at optimal policies around departure time. They also advocate for idle waiting both before and after service to avoid congestion. The mathematical formulation they describe without any congestion is also valid for the PRP, which is shown to perform better than that ofBektas¸

and Laporte (2011). The authors also study a special case where there is

only one vehicle and a fixed sequence of customers and proposed a specified algorithm for this problem. An adaptive large neighborhood search for this problem can be found inFranceschetti et al. (2017). In urban areas, the conditions around vehicle speeds are different to those of intercity travel. One way to calculate vehicle speed on a path between two customers is an arc-averaging method described byEhmke et al. (2016a). A time-dependent vehicle routing problem in urban areas is described and solved inEhmke et al. (2016b).

The choice of vehicles in the fleet also impacts fuel consumption, as each type of vehicle has its own specific parameters such as curb weight, engine friction factor, engine speed, etc.Koc¸ et al. (2014)study the extent to which the fleet choice matters by introducing and solving the fleet size and mix PRP, where a heterogeneous vehicle fleet is used. Saka et al.

(2017) study the PRP with a heterogeneous fleet of vehicles. Instead of

time windows, however, the proposed problem assumes that there are deadlines associated with each customer request.

Several studies apply different variants of the PRP to real or realistic problem instances. For instance,Soysal et al. (2015a)present an applica-tion based on distribuapplica-tion of fresh tomato for a company operating in western Turkey, where the distribution network has one distribution center and 11 supermarkets (customers). The authors solve an inventory routing problem for perishable items by considering environmental fac-tors and demand uncertainty. The results show that using consideration of perishability of items and fuel consumption reduces the total amount of emissions by 2%, but this leads to a 25.2% increase in the total cost.Soysal

et al. (2015b)conduct a case study for the distribution network of a

su-permarket chain operating in the Netherlands, where the distribution network consists of one depot, two satellites, and 16 customers. For this application, the authors extend the problem setting ofBektas¸ and Laporte

(2011) to a time-dependent, two-echelon CVRP formulation with

envi-ronmental considerations. The results indicate that using a fuel-minimizing objective function provides an average reduction of 2.5% on fuel consumption, but this comes at the expense of a 10.8% increase on cost. Soysal et al. (2016) extend the study of Soysal et al. (2015a) by

184

(17)

considering multiple products and multiple suppliers where horizontal collaboration is assumed between suppliers. They present a practical application for two suppliers, one of which distributes figs and the other cherries to five wholesale market halls (customers) using a 3PL company. The numerical evidence suggests that through horizontal collaboration a reduction of 17.1% and 29.3% can be achieved, on the total cost and the total amount of emissions, respectively. The final application we present here is byAlinaghian and Naderipour (2016) that is for a distribution operation of dairy products in the city of Esfahan in Iran, which includes one depot, 28 customers, and three vehicles. The case study is then formulated as a time-dependent vehicle routing problem with the objec-tive of reducing fuel consumption. The authors present numerical results suggesting that savings of around 21% can be reaped on fuel consumption.

3.1.3 Other Routing Problems

This section discusses other types of routing problems that explicitly incorporate environmental considerations. A list of the studies reviewed in this section is provided inTable 7.4.

One of the first studies that addresses CO2emissions within the VRP is

Palmer (2007), who investigates the effects of congestion on CO2

emis-sions. Kuo (2010) studies a VRP with time-dependent travel times for which the author develops a method to calculate fuel consumption and solves the problem using a simulated annealing algorithm. Figliozzi

(2010)describes an emissions-minimizing VRP, which incorporates

time-dependent travel speeds and time windows, for which a single objective and hierarchical multiobjective formulations are presented. The author describes heuristic algorithms for both versions of the problem. Along similar lines, Jabali et al. (2012) describe a time-dependent VRP that minimizes emissions. A tabu search method using a nearest-neighbor heuristic as a construction algorithm is described to solve the problem.

Mirzapour Al-e-hashem and Rekik, 2014present a multiproduct

multi-period inventory routing problem with a heterogeneous fleet of vehicles where greenhouse gas emissions are limited by a constraint. The authors propose a mixed-integer linear programming formulation to solve the proposed problem.Xiao and Konak (2015) introduce the green vehicle routing and scheduling problem with time-dependent travel times and time window constraints. The authors develop an MILP formulation of the problem and a three-stage solution approach for the solution with hierarchical objectives. They also describe a simulated annealing algo-rithm to solve large-size problem instances. Ehmke et al. (2016a) inves-tigate the effects of speed variability in relation to minimizing emissions on paths in urban areas. They assume that vehicles travel at traffic speed, using which they develop two data-driven approaches to find the shortest

(18)

TABLE 7.4 Other Green Routing Problems

Palmer (2007) Single Single H U U Micro P P D

Kuo (2010) Single Single H U Factor P P P

Figliozzi (2010) Single Multi E& H U U Macro P e P

Jabali et al. (2012) Single Single H U Macro P e D

Mirzapour Al-e-hashem and Rekik, 2014

Single Single H Factor P e e

Xiao and Konak (2015)

Single Multi E& H U U Factor P e e

Ehmke et al. (2016a) Single Single H U U Macro P P P

C¸ imen and Soysal (2017)

Single Single H U U Macro P e P

Maden et al. (2010) Single Single H U U U Macro P e P

Figliozzi (2011) Single Multi H U U U Macro P e D

Qian and Eglese (2014)

Single Single H U U U Macro P e D

Soysal and C¸ imen (2017)

Single Single H U U Macro P e P

Aranda et al. (2012) Single Single H U LCA e e e

Oberscheider et al. (2013)

Single Single E& H U U U Factor e e P

186

(19)

paths that minimize fuel consumption, namely path and arc-averaging methods. C¸ imen and Soysal (2017) study a similar problem by consid-ering stochastic vehicle speeds and a different macroscopic emission model.

Other applications reported for routing problems with an explicit consideration to minimize negative environmental impacts are as follows.

Maden et al. (2010)describe a case study for the distribution system of an

electric goods wholesaler operated in the southwest of the United Kingdom, for deliveries made over 9 days and where the number of customers visited ranges between 40 and 64 each day. A heuristic algo-rithm based on tabu search is used to solve the problem. Through a computational study, the authors report around 7% savings on CO2

emissions. Figliozzi (2011) studies the same problem introduced in an earlier study (Figliozzi, 2010) by analyzing CO2emissions for different

levels of congestion and time-definite customer demands. The author also carries out a case study in Portland, United States. An algorithm that consists of a route construction and a route improvement phase is described to solve the problem, using which the author analyzes the impact of different speed levels and different depot locations on emis-sions.Qian and Eglese (2014)focus on a problem that finds paths with the least fuel consumption, where vehicle speeds are time-dependent. The authors also conduct a case study with 14 customers and one depot located in Bristol, United Kingdom. The authors describe a time-increment-based dynamic programming algorithm and a new heuristic method consisting of a route selection and a speed adjustment stage. The application of the algorithms leads to about 6%e7% savings in emissions.

Soysal and C¸ imen (2017)concern a distribution system operating over a

pharmaceutical warehouse and 15 pharmacies in Ankara, Turkey. The application of a simulation-based restricted dynamic programming approach as a solution approach indicates that if the vehicles avoid heavily congested periods in serving the pharmacies, then savings of 2.3% can be achieved on the total amount of emissions. Other application-based studies areAranda et al. (2012)andOberscheider et al. (2013).

3.2 Tactical Decision Making

This section reviews studies concerning tactical decisions such as location-routing and allocation problems.

3.2.1 Location-Routing Problems

The first class of problems we review here is those that consider a joint treatment of location and routing decisions. The literature on such problems is still in its infancy when an explicit consideration of

(20)

environmental performance of the transportation activities is concerned.

Table 7.5provides a summary of the existing papers.

The first two of the studies listed inTable 7.5address the location and routing decisions as part of a green network design problem. In particular,

Cachon (2014)looks at a retail store supply chain problem by considering

CO2emissions, where the objective is to minimize the transportation cost,

which includes costs relevant to operating vehicles, fuel consumption and emissions, and space (store) cost. A two-echelon network is considered with a warehouse, retailers, and customers. To replenish the inventories, retailers travel to warehouses, which formulated as a traveling salesman problem, whereas the distribution problem for the customer modeled as a continuous version of a p-median problem, to which inventory decisions are linked. The problem compares small local shops and big retailers with regards to this objective. The second study is byGovindan et al. (2014), who describe a two-echelon location-routing problem with time windows for a perishable food supply chain network with manufacturers, distri-bution centers, and retailers. The model consists of two objective func-tions; to minimize the total cost and minimize the total environmental impact. The authors describe a multiobjective hybrid approach to solve a problem that combines two multiobjective algorithms, namely a multi-objective particle swarm optimization and a multimulti-objective variable neighborhood search.

Koc¸ et al. (2016)analyze the impact of location, fleet composition, and

routing on emissions in urban freight transportation. In this study, speed is not considered to be a decision variable in this problem but rather determined on the basis of different speed zones that cities are assumed to be divided into. The authors describe a location-routing problem with a heterogeneous fleet of vehicles in a city logistics concept. The problem is solved by means of an adaptive large neighborhood search algorithm. On the basis of randomly generated but structured instances, the findings suggest that the depot locations are generally selected to be farther away from city centers even if this increases the distance, mainly due to being able to drive faster than the slow speeds assumed in city centers.Toro

et al. (2017) present a biobjective green capacitated location-routing

problem where the two objective functions minimize the operational cost and fuel consumption and CO2 emission, respectively. The

ε-constraint method is used to solve the corresponding biobjective mathematical model.

Zhalechian et al. (2016)study a real-life application that is based on a

supply chain of LCD and LED televisions assuming a two-echelon network. The network consists of 20 cities in Iran, each of which is a demand point, seven candidate depot locations, and two suppliers. For this application, the authors introduce a sustainable closed-loop location-routing inventory problem under mixed uncertainty where the objectives

188

(21)

TABLE 7.5 Tabulated Summary of Location-Routing Problems Incorporating Environmental Concerns

Cachon (2014) Multi Single E Factor P e e

Govindan et al. (2014)

Multi Multi H U Factor e e e

Koc¸ et al. (2016) Single Single E& H Micro P D P

Toro et al. (2017) Single Multi E Macro P D P

Zhalechian et al. (2016)

Multi Multi H U U Micro P D e

Tricoire and Parragh (2017)

Single Multi E& H U Factor P D e

3. GREEN NETWORK DESIGN PR OBLEMS APPROXIM A TION T O SUST AINABLE TRANSPO R T A TION

(22)

are to: (1) minimize the total cost; (2) minimize the environmental impact of CO2emissions, fuel consumption, and wasted energy; and (3)

maxi-mize the social impact of the closed-loop supply chain. The authors present a stochastic-possibilistic programming formulation of the prob-lem that treats some of the uncertainty through the use of fuzzy param-eters, and propose a new hybrid two-stage solution algorithm. The last study we review in this section is the one byTricoire and Parragh (2017), who describe a green city hub location-routing problem which is an extension of the location-routing problem with a heterogeneous fleet with two objectives; to minimize the total cost and minimize CO2emissions.

Solutions are obtained by decomposition that first generates vehicle routes which are fed into a set covering model solved using a biobjective branch-and-bound algorithm. The authors test their algorithm on in-stances obtained from industrial partners in Austria that include 22 hubs, 898 or 1635 customers, and two or seven vehicle types. The authors conclude by suggesting that investing in facilities reduces pollution by showing trade-offs with cost.

3.2.2 Allocation Problems

Problems arising at a tactical level of decision making also include those of allocation, in which decisions concern the assignment of cus-tomers to facilities (or depots) at given locations. In multiechelon net-works, allocation decisions are made at each echelon. For example, in a two-echelon network with suppliers, distribution centers, and retailers, the allocation decisions include the assignment of distribution centers to the suppliers and the retailers to the distribution centers. Table 7.6 pre-sents an overview of the studies of such problems with an explicit aim of reducing negative environmental impacts of transportation activities.

Each study shown inTable 7.6gives rise to a different formulation of the relevant problem. Rather than presenting the individual formulations, we provide below a general representative model that serves as a framework of allocation problems where environmental indicators are represented in a minimizing objective function using cost measures. The problem is defined on a directed graph where N is the set of nodes con-sisting of a set of suppliers, distribution centers, and retailers denoted, with the corresponding nodes denoted by the sets S, D, R, respectively. Each distribution center j˛ D has a storage capacity Cjand each retailer k

˛ R has demand Dk. The unit transportation and CO2emissions cost per a

unit distance are denoted by ctand cco, respectively, where dijrepresents

the distances between two different nodes i and j. The decision variables of the formulation are defined as follows: Non-negative continuous var-iables fij and gij represent the amount of commodity carried between a

supplier i˛ S and a distribution center j ˛ D, and a distribution center j ˛

190

(23)

Paksoy and O¨ zceylan (2014)

Multi Single E Macro P e D

Soysal et al. (2014) Multi Multi E U Factor P D e

Neto et al. (2008) Multi Multi E U LCA e D e

Neto et al. (2009) Multi Multi H U LCA e D e

Bing et al. (2014) Multi Single E U Factor P D e

Kim et al. (2009) Single Multi H U Macro P D P

Bauer et al. (2010) Single Single E U Macro P D P

Pan et al. (2013) Multi Single E U Macro P D P

Qu et al. (2016) Single Single E U Factor P D e

Demir et al. (2016) Single Single E& H U U U Micro e D e

Nagurney et al. (2007)

Multi Multi E Factor e D e

Cruz and Matsypura (2009)

Multi Multi E Factor e D e

3. GREEN NETWORK DESIGN PR OBLEMS AN APPROXIM A TION T O SUST AINABLE TRANSPO R T A TION

(24)

D and a retailer k ˛ R, respectively. A generic formulation for a basic allocation problem is as follows:

MinimizeX i˛P X j˛D fijdijðccoþ ctÞ þ X j˛D X k˛C gjkdjkðccoþ ctÞ (7.28) subject to X i˛P fij Cj cj˛D (7.29) X j˛D gjk¼ Dk ck˛R (7.30) X i˛P fij X k˛R gjk¼ 0 cj˛D (7.31) fij 0 ci˛P; j˛D (7.32) gjk 0 cj˛D; k˛R (7.33)

The objective function (7.28) minimizes the total transportation and CO2emissions cost. Constraint(7.29)imposes capacity limits on the

dis-tribution centers. Constraint (7.30) ensures that the demand of each customer is fully met. Constraint(7.31)guarantees that all demand sent to a distribution center will be distributed to the customers allocated to that distribution center. Constraints (7.32) and (7.33) are the non-negativity restrictions on the decision variables.

Several studies look at allocation problems on variations or extensions of the formulation above. For example,Paksoy and O¨ zceylan (2014)study a supply chain network design problem that minimizes the costs relevant to transportation, noise pollution, CO2emissions, and fuel consumption.

The authors present an integer nonlinear programming formulation of the problem. Soysal et al. (2014) consider a food logistics network design problem for which they present a multiobjective linear programming model. The objectives are to minimize the total logistics cost and to minimize the total GHG emissions. The authors use the ε-constraint method to identify the Pareto frontier, and present a real-life application for a beef logistics network in Brazil exporting products to the European Union.

Some studies include reverse logistics activities in the green network design problems. In such settings, end-of-life facilities are explicitly rep-resented in the network, at which point the products are recycled and sent onwards to the suppliers.Neto et al. (2008)look at design and evaluation of sustainable logistics network structures using a multiobjective opti-mization model in which the objectives relate to minimizing cost and environmental impacts. They describe a new technique to evaluate the

192

(25)

efficiency of existing networks that exploits the similarities between data envelopment analysis and multiobjective programming. The European pulp and paper industry is used as a case study.Neto et al. (2009)study a similar problem where they propose a two-phase heuristic algorithm to find an approximation to the Pareto frontier, using a recycling logistics network in Germany as a real-life application of the problem.Bing et al.

(2014)describe a sustainable reverse logistic network design problem for

a multilevel network with multiple products, using a case study arising in the separation of plastic waste operations in the Netherlands.

Within the context of tactical level planning problems, there are studies that assume the use of different transportation modes on more complex networks where each mode of transportation has its own set of parame-ters, such as capacity and emissions. For example,Kim et al. (2009)study a biobjective design problem on a multimodal hub and spoke network where the objectives are to minimize transport cost and CO2emissions

and solved using theε-constraint method. The authors apply the method to a problem arising in a real-life freight distribution network connecting the ports of Rotterdam in the Netherlands and Gdansk in Poland. One other such study is by Bauer et al. (2010) on designing an intermodal freight network. The authors describe a large-scale integer linear pro-gramming formulation of the problem, and apply it on an intermodal network operating over Austria, the Czech Republic, and Poland. Pan

et al. (2013), Qu et al. (2016), andDemir et al. (2016)are other studies that

consider different transportation modes.

Some studies on these problems apply game theoretic models.

Nagurney et al. (2007), for example, look at a transportation network

design problem arising in a supply chain with two objectives, one maxi-mizing profit and the other minimaxi-mizing emissions. The authors derive optimality and equilibrium conditions for the problem. Cruz and

Matsypura (2009)study a supply chain network design problem to which

corporate social responsibility considerations are incorporated.

3.3 Strategic Decision Making

This section analyzes the studies in which long-term strategic decisions are made, such as those concerning facility location, with explicit envi-ronmental concerns in mind.Table 7.7presents an overview of the rele-vant studies in this area, which we describe in further detail below.

Ghaddar and Naoum-Sawaya (2012)study a facility location problem

with market competition in which market prices and production costs are decided based on economic equilibrium. The authors impose a limit on emissions by considering a carbon trading mechanism.Xifeng et al. (2013)

(26)

TABLE 7.7 Strategic Location Problems With Environmental Concerns Defined on Single Echelon Networks

Ghaddar and Naoum-Sawaya (2012)

Single Single E U Factor e D e

Xifeng et al. (2013) Single Multi H Factor P P e

Treitl and

Jammernegg (2014)

Single Single E& H U Factor P D e

Harris et al. (2014) Single Multi E& H Factor P e e

Khoei et al. (2017) Single Single E U U Micro P P D

Mohammadi et al. (2014)

Single Multi E& H U Micro P D P

Niknamfar and Niaki (2016)

Single Multi H U Micro P P D

194

(27)

objective functions are to minimize cost, to minimize CO2emissions, and

to maximize minimum service reliability. The problem is solved by a heuristic hybrid algorithm that uses theε-constraint method. Treitl and

Jammernegg (2014)study two problems that include location-allocation

decisions, namely the p-median and the warehouse location problem, where environmental and economic impacts of transportation activities are minimized. Harris et al. (2014) solve a capacitated facility location-allocation problem using multiobjective optimization where the objec-tive functions are to minimize the total cost and to minimize the CO2

emissions. Solutions are obtained using a mixed integer linear program-ming formulation and a heuristic that combines a multiobjective evolu-tionary algorithm for the location decisions and Lagrangian relaxation for the allocation decisions. Khoei et al. (2017) describe a green Weber problem and time-dependent version of the same, where the decisions concern the location of a single facility, as well as the speeds of the ve-hicles sent to customers, so that the total amount of CO2 emissions is

minimized. Second-order cone programming formulations are described for both problems.

There are a couple of studies that look at environmental considerations within hub location problems. In particular, Mohammadi et al. (2014)

describe a sustainable hub location problem with three objectives, namely to minimize transportation costs, to minimize the total cost of noise pollution, and to minimize the fuel consumption on arcs and at hubs.

Niknamfar and Niaki (2016)describe a biobjective hub location problem

assuming collaboration between a holding company and multiple car-riers. The objective function maximizes the profits for both the company and the carriers. Fuel consumption and CO2emissions are modeled as tax

for carriers in the objective function.

As for other strategic location(-allocation) problems that appear in the literature on multiechelon networks, we present a summary inTable 7.8

and discuss these references in further detail below.

Hugo and Pistikopoulos (2005)describe a supply chain design network

problem with the consideration of LCA principles and using multiple objective functions. The objectives are to maximize the net present value and to minimize the environmental impact. The authors propose a mul-tiobjective mixed integer linear programming formulation and use the ε-constraint method to find the efficient frontier. Wang et al. (2011)

consider environmental investment decisions for facilities with two objective functions; to minimize the total cost and minimize CO2

emis-sions from facilities and transportation activities.Elhedhli and Merrick

(2012)study a two-echelon supply chain network design problem, where

the objective is to minimize the costs of installation, handling, trans-portation, and CO2 emissions. The solution algorithm combines

(28)

TABLE 7.8 Strategic Location Problems With Environmental Concerns Defined on Multiechelon Networks

Hugo and Pistikopoulos (2005)

Multi Multi E U LCA P e e

Wang et al. (2011) Multi Multi E U Factor P D e

Elhedhli and Merrick (2012)

Multi Single H Factor P D P

Mallidis et al. (2012) Multi Multi E U Factor e D e

Kadzinski et al. (2017) Multi Multi E& H U Factor e D e

Varsei and Polyakovskiy (2017)

Multi Multi E U Factor e D e

Pishvaee and Razmi (2012) Multi Multi E U U LCA e D e

Miranda-Ackerman et al. (2017)

Multi Multi E U LCA e D e

Chaabane et al. (2011) Multi Multi E U Factor P D e

Abdallah et al. (2012) Multi Single E U LCA P D e

Chaabane et al. (2012) Multi Multi E LCA e D e

Shaw et al. (2016) Multi Single E U Factor e D e

Rezaee et al. (2017) Multi Single E U U Factor e D e

Guillen-Gosalbez and Grossman (2009)

Multi Multi E U U LCA P D e

Bojarski et al. (2009) Multi Multi E U LCA P e e

Duque et al. (2010) Multi Multi E U LCA e D e

Pinto-Varela et al. (2011) Multi Multi E U LCA P e e

You et al. (2012) Multi Multi E U LCA P D e

196

(29)

supply chain network design problem in which the decisions concern the selection of the port of entry and transportation mode, and where the authors analyze the impact of using dedicated and shared warehouses on cost and emissions on a real-life application in southeast Europe.

Kadzinski et al. (2017)revisit a case study that was looked at byMallidis

et al. (2012), by casting the problem as a multiobjective green supply chain

problem. The objectives separately minimize the total cost, total amount of CO2emissions, and the total amount of particulate matters emitted. In

addition to using exact methods such as the weighted sum and epsilon constraint scalarization, the authors apply two well-known multiobjective evolutionary algorithms, namely SPEA2 and NSGA-II, and devise an interactive solution mechanism that incorporates the indirect preferences of a decision maker. Varsei and Polyakovskiy (2017) study a multi-objective sustainable supply chain network design problem where the objective is to minimize the economical, environmental, and social im-pacts of the supply chain for a top wine company in Australia. The au-thors develop a customized model solved by an augmentedε-constraint method. Other similar studies are due toPishvaee and Razmi (2012)and

Miranda-Ackerman et al. (2017).

Similar to those discussed in previous sections, some studies make use of a carbon trading mechanism to minimize emissions.Chaabane et al.

(2011)is one such studies, which uses goal programming to solve a

bio-bjective network design problem minimizing total cost and the total amount of CO2emissions are minimized.Abdallah et al. (2012)propose a

carbon-sensitive supply chain problem using green procurement strate-gies, where a single objective function minimizes the sum of the fixed costs, distribution costs, procurement costs, and emissions costs related to the carbon trading mechanism. Chaabane et al. (2012) present a bio-bjective sustainable supply chain network design problem under an emission trading mechanism that includes reverse logistics activities. Other studies that consider a carbon trading mechanism areShaw et al.

(2016)andRezaee et al. (2017), both of which study green network design

problems under uncertainty.

A number of studies have a particular focus on the design chemical supply chains with environmental consideration. For example,

Guillen-Gosalbez and Grossman (2009) describe a sustainable chemical

supply chain design problem where the objectives are to maximize the net present value and minimize the environmental impacts based on LCA principles. The authors formulated the problem as a bicriterion stochastic mixed integer nonlinear programming model, which is then reformulated as a parametric mixed integer nonlinear programming model. Other similar studies are due toBojarski et al. (2009), Duque et al. (2010),

(30)

3.4 Other Studies

In conducting this review, a number of papers were identified that did not necessarily focus on decision (optimization) problems arising in lo-gistics network planning, but rather provided broader discussions and insights into green applications. For this reason, we review them here separately as opposed to being part of the three-level classification of decision-making. For example, some studies discuss the use of comput-erized routing and scheduling as well as vehicle telematics for reducing emissions (e.g., Le´onardi and Baumgartner, 2004; Baumgartner et al., 2008). Others discuss the need to use geographical information system software in vehicle routing such as GIS, ArcGIS, and GPS (e.g.,Ericsson et al., 2006; Apaydin and Gonullu, 2008; Tavares et al., 2009; Jovicic et al.,

2010; Zsigraiova et al., 2013; Bandeira et al., 2013).Wu and Dunn (1995)

and Aronsson and Huge Brodin (2006)evaluate the effect of innovative

ideas, strategies, or structural changes on the environment.Beltran et al.

(2009)propose a transit network design problem with green vehicles that

produce lower emissions. Since the number of green vehicles is limited, they are only assigned to specific routes.

The use of other types of methods within green network design are discussed in various references, such as simulation (Van Der Vorst et al., 2009), analytic network process (Dou and Sarkis, 2010), constant factor approximation algorithms (Gaur et al., 2013), and fuzzy-based ap-proaches (Cirovic et al., 2014; Jovanovic et al., 2014).

4. CONCLUSIONS AND THOUGHTS ON FURTHER

RESEARCH

Given the increasing concerns on impacts of transportation, logistics, and supply chain activities on the environment, the existing body of research is continually developing and expanding at a significant pace. This review has identified most of these studies to be on operational as-pects, such as vehicle routing and scheduling, which are short-term plans for such activities. The work on integrating environmental concerns, although growing, is less developed at tactical and strategic levels of decision making, and as such it will be important to understand the im-plications of longer-term decisions, such as facility location, customer allocation, and transport mode choice, on the environment as well as on the economic viability of the underlying logistics system.

Despite their common and widespread use, the use of the terms “green” and “sustainability” present a certain degree of ambiguity. We do not claim to have offered, or even attempted, a complete clarification between the uses of these terms here as such discussions are beyond the

198

(31)

scope of this review. However, in the way of taking some steps towards such a clarification, at least in the context of green network design, we have assumed “green” design activities to be a class of “sustainable” design activities. We have assumed that green pertains to an explicit goal of reducing emissions in designing logistics networks.

This review has highlighted that a good portion of the relevant OR literature in this field makes use of multiobjective optimization tools in formulating, solving, and analyzing green network design problems. This is not entirely surprising given the ability of multiobjective optimization tools to allow for separate treatment of various objectives that are not all necessarily commensurable (e.g., cost in monetary units vs. emissions in grams). This is all the more important as not all environmental consid-erations can be measured in monetary units. Such tools also allow iden-tifying the trade-offs between what seem to be conflicting objectives, although in some cases there may be winewin situations.

A common way in dealing with green network design problems seems to be an explicit integration of the environmental factors, such as emis-sions, noise pollution, carbon trading mechanisms, and energy usage, into the existing models of such problems. This typically manifests itself in the form of an augmented (and often more complicated) objective function(s), where the aim is often to minimize the environmental consequences along with the traditional operational cost measures. The one aspect that comes across clearly from a methodological point of view is that such in-tegrations give rise to problem extensions that are often as challenging, if not more difficult, to solve. Most of the solution algorithms, which have been described for the solution of such problems, seem to be modifica-tions of the existing ones.

The explicit goal of reducing emissions assumes the availability of models that adequately capture the type of factors affecting fuel con-sumption that is inherently linked to emissions, the degree to which such factors affect fuel usage and the accuracy of estimations. Whilst there is a good body of work on this aspect, offering models that range from macroscopic to microscopic, from factor models and wide-area assess-ment tools, there is still some room for studies that offer empirical evi-dence as to the accuracy of such models. These models are generally used for operational activities. The consideration of higher-level design prob-lems such as facility location require a good understanding of the emis-sions caused by the processes within such entities (e.g., energy use within manufacturing facilities or container ports), which also need further investigation.

Finally, we mention the importance of the choice of transport mode in designing distribution networks, given the unique characteristics and environmental performance of each individual mode of transport. Modal shift, a term that has long been known and discussed within logistics to

(32)

reduce the environmental externalities, can be captured at sufficient levels of detail within strategic and tactical decision-making problems discussed above, which would allow for assessing the trade-offs associated with shifting of freight on economic and environmental measures of performance.

References

Abdallah, T., Farhat, A., Diabat, A., Kennedy, S., 2012. Green supply chains with carbon trading and environmental sourcing: formulation and life cycle assessment. Applied Mathematical Modelling 36 (9), 4271e4285.

Alinaghian, M., Naderipour, M., 2016. A novel comprehensive macroscopic model for time-dependent vehicle routing problem with multi-alternative graph to reduce fuel consump-tion: a case study. Computers& Industrial Engineering 99, 210e222.

Androutsopoulos, K.N., Zografos, K.G., 2017. An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations. Transportation Research Part C: Emerging Technologies 82, 180e209.

Apaydin, O., Gonullu, M.T., 2008. Emission control with route optimization in solid waste collection process: a case study. Sadhana 33 (2), 71e82.

Aranda, U.A., Ferreira, G., Bribia´n, Z.I., Va´squez, Z.D., 2012. Study of the environmental per-formance of end-of-life tyre recycling through a simplified mathematical approach. Ther-mal Science 16 (3), 889e899.

Aronsson, H., Huge Brodin, M., 2006. The environmental impact of changing logistics structures. The International Journal of Logistics Management 17 (3), 394e415. Bandeira, J., Almeida, T.G., Khattak, A.J., Rouphail, N.M., Coelho, M.C., 2013. Generating

emissions information for route selection: experimental monitoring and routes characterization. Journal of Intelligent Transportation Systems 17 (1), 3e17.

Bauer, J., Bektas¸, T., Crainic, T.G., 2010. Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design. Journal of the Operational Research Society 61 (3), 530e542.

Baumgartner, M., Le´onardi, J., Krusch, O., 2008. Improving computerized routing and sched-uling and vehicle telematics: a qualitative survey. Transportation Research Part D: Trans-port and Environment 13 (6), 377e382.

Bektas¸, T., Laporte, G., 2011. The Pollution-Routing problem. Transportation Research Part B: Methodological 45 (8), 1232e1250.

Beltran, B., Carrese, S., Cipriani, E., Petrelli, M., 2009. Transit network design with allocation of green vehicles: a genetic algorithm approach. Transportation Research Part C: Emerging Technologies 17 (5), 475e483.

Bernstein, L., Bosch, P., Canziani, O., Chen, Z., Christ, R., Riahi, K., 2008. IPCC, 2007: Climate Change 2007: Synthesis Report. IPCC, Geneva. Available from:https://www.ipcc.ch/ pdf/assessment-report/ar4/syr/ar4_syr_full_report.pdf. isbn:2-9169-122-4.

Bing, X., Bloemhof-Ruwaard, J.M., van der Vorst, J.G., 2014. Sustainable reverse logistics network design for household plastic waste. Flexible Services and Manufacturing Journal 26 (1e2), 119e142.

Bojarski, A.D., Laı´nez, J.M., Espun˜a, A., Puigjaner, L., 2009. Incorporating environmental im-pacts and regulations in a holistic supply chains modeling: an LCA approach. Computers & Chemical Engineering 33 (10), 1747e1759.

Brandenburg, M., Govindan, K., Sarkis, J., Seuring, S., 2014. Quantitative models for sustain-able supply chain management: developments and directions. European Journal of Oper-ational Research 233 (2), 299e312.